CFA Level I Exam · Pricing and Valuation of Interest Rate and Other Swaps

Currency Swaps Pricing and Valuation Explained Step by Step

Updated 7 October 2026 · Fact-checked

A currency swap exchanges principal and interest in two currencies. Price it by finding each currency's fixed rate from its own discount factors: (1 − final factor) ÷ sum of factors. Value it later by valuing each leg as a bond in its own currency, converting at the current spot rate, and taking the difference.

Understand Currency Swaps Pricing and Valuation

A currency swap is a contract where two parties exchange cash flows in two different currencies. Say a US firm needs euros and a eurozone firm needs dollars. They swap notional principals at the start, pay interest to each other during the life of the swap, and swap the principals back at maturity.

This is the key difference from an interest rate swap. In an interest rate swap, both legs use the same currency, so the notional is never exchanged and only the net interest is paid. In a currency swap, the two legs are in different currencies, so interest is usually paid in full on each leg, and the notional is normally exchanged at both start and end. The notional amounts are linked by the spot rate at initiation.

There are four common structures: fixed-for-fixed, floating-for-floating, fixed-for-floating and floating-for-fixed. Each leg is just a bond in its own currency. One party is long one bond and short the other.

To price the swap, you set the fixed rate in each currency so that the swap has zero value at the start. You do this separately in each currency, using that currency's own discount factors. The spot rate does not enter the fixed rate calculation. It only converts the notional.

To value the swap later, you value each leg in its own currency using today's discount factors, convert one leg into the other currency at today's spot rate, and subtract. A floating leg that has just reset is worth its notional (plus the next coupon, discounted).

Key formulas to remember

Notional in the second currency: Notional (USD) = Notional (EUR) × S0, where S0 is USD per 1 EUR; Use the spot rate at initiation. Check the quote direction: multiply when the rate is price of the notional currency in the other currency.
Periodic fixed rate for each currency: Fixed rate per period = (1 − Z_N) ÷ (Z_1 + Z_2 + … + Z_N); Z are discount factors for that currency. Annual rate = periodic rate × periods per year. Do it once per currency.
Value of a fixed leg (own currency): PV = C × (Z_1 + … + Z_N) + Notional × Z_N; C is the fixed coupon per period in currency units. Use current discount factors.
Value of a floating leg at a reset date: PV = Notional (today, just reset); Between resets: PV = (Notional + next floating payment) × Z for the time to the next payment.
Value of the swap to the receiver of currency A: V (in currency B) = PV(leg A, in A) × S_t (B per A) − PV(leg B, in B); Convert only the leg stated in currency A, so the result is in currency B. Leg B is already in B and is not converted. Use the spot rate at time t, not at initiation.

How to solve Currency Swaps Pricing and Valuation questions

Use this order for any pricing or valuation question on a currency swap.

1Identify the structure: which legs are fixed or floating, in which currencies, and which party pays or receives each leg.
2Write the notionals in both currencies. Link them with the initiation spot rate if only one is given.
3For pricing, compute the fixed rate separately in each currency: (1 − final discount factor) ÷ sum of discount factors. Multiply by periods per year to annualize.
4For valuation, list the remaining cash flows of each leg: coupons, and the final notional.
5Discount each leg in its own currency using the current discount factors for that currency. Treat a just-reset floating leg as worth its notional.
6Convert one leg to the other currency at the current spot rate. Do not use the initiation spot rate.
7Subtract the leg you pay from the leg you receive. Check the sign and the currency of the answer.
8Sense check: if rates and spot are unchanged since initiation, the value should be near zero.

Quickest way: Leg-by-leg bond shortcut

When to use it: Use it for almost every numerical question. It avoids long cash flow tables and keeps you inside 90 seconds.

Add up the discount factors once and store the sum (BA II Plus: type the sum, press STO 1; HP 12C: STO 1).
Fixed rate = (1 − last factor) ÷ stored sum. On the BA II Plus: 1 − last factor = ÷ RCL 1 =. On the HP 12C: 1 ENTER last factor − RCL 1 ÷.
For a valuation, multiply the final payment (notional plus last coupon) by the last factor when there is only one period left.
Treat a freshly reset floating leg as par. This often removes a whole leg of work.
Convert at the current spot and eliminate options with the wrong sign or those that used the old spot rate.

Common mistakes in Currency Swaps Pricing and Valuation

Using the spot rate in the fixed rate formula.
Students think a currency swap rate must reflect the exchange rate.
Fix: Price each currency's fixed rate only from that currency's discount factors. The spot rate only converts notionals and values.
Using the initiation spot rate when valuing the swap later.
The notional was set at the initiation rate, so it feels like the rate to use.
Fix: Use the notionals as fixed, but convert the present values at the current spot rate.
Discounting both legs with one discount curve.
It is easy to reuse the first curve you set up.
Fix: Discount each leg with the curve of its own currency.
Forgetting the final notional exchange.
Interest rate swaps never exchange notionals, so the habit carries over.
Fix: Add the notional to the last cash flow of each fixed leg. In a currency swap, the notional is a real cash flow.
Getting the sign wrong.
Students mix up which leg the party receives.
Fix: Value = PV of what you receive minus PV of what you pay, in one currency. Write receive and pay next to each leg first.
Treating the floating leg as worth par at any date.
The par rule is learned for the reset date only.
Fix: Between resets, value it as (notional + next floating payment) discounted over the time left to that payment.

Worked examples

Example 1

A two-year annual-pay fixed-for-fixed USD/EUR currency swap is being priced. USD discount factors are 0.9709 (1 year) and 0.9426 (2 years). EUR discount factors are 0.9804 (1 year) and 0.9612 (2 years). What are the fixed rates on the USD leg and the EUR leg? Choices: A. USD 2.00%, EUR 3.00%; B. USD 3.00%, EUR 2.00%; C. USD 3.00%, EUR 3.00%.

Show the solution

USD sum of factors = 0.9709 + 0.9426 = 1.9135.
USD fixed rate = (1 − 0.9426) ÷ 1.9135 = 0.0574 ÷ 1.9135 ≈ 0.0300, or 3.00%.
EUR sum of factors = 0.9804 + 0.9612 = 1.9416.
EUR fixed rate = (1 − 0.9612) ÷ 1.9416 = 0.0388 ÷ 1.9416 ≈ 0.0200, or 2.00%.
The two rates differ because the discount curves differ. That removes A and C.

Answer: B. USD 3.00%, EUR 2.00%.

Example 2

One year ago a firm entered a 2-year annual-pay fixed-for-fixed currency swap. It receives 2.00% on €10,000,000 and pays 3.00% on $11,000,000 (initial spot $1.10 per €). One year remains. The 1-year discount factors are 0.9804 for EUR and 0.9615 for USD. The spot rate is now $1.20 per €. What is the swap's value to the firm in USD? Choices: A. −$893,715; B. $1,106,301; C. $1,893,795.

Show the solution

Remaining EUR receipt in 1 year = €10,000,000 × 1.02 = €10,200,000.
PV of EUR leg = €10,200,000 × 0.9804 = €10,000,080.
Convert at today's spot: €10,000,080 × 1.20 = $12,000,096.
Remaining USD payment in 1 year = $11,000,000 × 1.03 = $11,330,000.
PV of USD leg = $11,330,000 × 0.9615 = $10,893,795.
Value = $12,000,096 − $10,893,795 = $1,106,301.
A comes from 10,000,080 − 10,893,795 = −893,715. This subtracts euros from dollars without converting the EUR leg, so it mixes currencies. It is also negative, so it has the wrong sign.
C does not come from a consistent calculation: the correct value is $1,106,301, so C is too large. Always check that both legs are in one currency before you subtract.

Answer: B. $1,106,301 in favor of the firm, because the euro has strengthened against the dollar.

Exam tips

Questions are standalone with three options, so first decide the sign and rough size of the answer. This often removes two options.
Check whether the question asks for a rate, a present value, or a value in a specific currency before you calculate.
Expect distractors from the common mistakes: wrong spot rate, one curve for both legs, a missing notional exchange, and a flipped sign.
Know the contrast with an interest rate swap: different currencies, notional exchanged, interest not netted.
Read the spot quote carefully. 'USD per EUR' means multiply euro amounts by the rate to get dollars.

Practice questions from Pricing and Valuation of Interest Rate and Other Swaps

Currency Swaps Pricing and Valuation in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Currency Swaps Pricing and Valuation: frequently asked questions

What is the difference between a currency swap and an interest rate swap?

In an interest rate swap both legs are in one currency, the notional is not exchanged, and only the net interest is paid. In a currency swap the legs are in two currencies, the notionals are normally exchanged at the start and end, and interest is paid in each currency.

How do you calculate the fixed rate on a currency swap?

Use the discount factors of one currency: fixed rate per period = (1 − last discount factor) ÷ sum of all discount factors. Repeat for the other currency. Multiply by the number of periods per year to annualize.

How do you value a currency swap after it starts?

Value each leg as a bond in its own currency using current discount factors. A floating leg that has just reset is worth its notional. Convert one leg at today's spot rate and subtract the leg you pay from the leg you receive.

Is the notional exchanged in a currency swap?

Usually yes, at initiation and again at maturity, using the initial spot rate. Variants exist where the initial exchange is skipped, so read the question for what it states.